Not yet reviewed by Pith; the record is open.

Observational systematics complicate comparisons with theoretical models limiting understanding of galaxy evolution. In particular, different empirical determinations of the stellar mass function imply distinct mappings between the galaxy and halo masses, leading to diverse galaxy evolutionary tracks. Using our state-of-the-art STatistical sEmi-Empirical modeL, STEEL, we show fully self-consistent models capable of generating galaxy growth histories that simultaneously and closely agree with the latest data on satellite richness and star-formation rates at multiple redshifts and environments. Central galaxy histories are generated using the central halo mass tracks from state-of-the-art statistical dark matter accretion histories coupled to abundance matching routines. We show that too flat high-mass slopes in the input stellar-mass-halo-mass relations as predicted by previous works, imply non-physical stellar mass growth histories weaker than those implied by satellite accretion alone. Our best-fit models reproduce the satellite distributions at the largest masses and highest redshifts probed, the latest data on star formation rates and its bi-modality in the local Universe, and the correct fraction of ellipticals. Our results are important to predict robust and self-consistent stellar-mass-halo-mass relations and to generate reliable galaxy mock catalogues for the next generations of extra-galactic surveys such as Euclid and LSST.